This paper deals with the block encoding of discrete, memoryless sources with equiprobable outputs subject to a fidelity critereon. The encoder is assumed to be deterministic and a lower bound is derived on the amount of computational work required to encode such sources as a function of the code rate and fidelity of the encoding. An example is given to show that the bound cannot be substantial...

We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. This procedure is illustrated using a ZZ lattice. We also evaluate i...

We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on rate-distortion theory and the theory of finite point processes. We introduce fundamental information-theoretic concepts and quantities for point processes and ...

Estimating optimal phylogenetic trees or hierarchical clustering trees from metric data is an important problem in evolutionary biology and data analysis. Intuitively, the goodness-of-fit of a metric space to a tree depends on its inherent treeness, as well as other metric properties such as intrinsic dimension. Existing algorithms for embedding metric spaces into tree metrics provide distortio...

A new class of harmonic multivalent functions defined by an integral operator is introduced. Coefficient inequalities, extreme points, distortion bounds, inclusion results and closure under an integral operator for this class are obtained .

In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on...

A necessary and sufficient coefficient is given for functions in a class of complexvalued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.

We define and investigate a new class of Sǎlǎgean-type harmonic multivalent functions. we obtain coefficient inequalities, extreme points and distortion bounds for the functions in this class. 2000 Mathematics Subject Classification: 30C45, 30C50, 31A05.

We define and investigate a new class of Salagean-type harmonic multivalent functions. we obtain coefficient inequalities, extreme points and distortion bounds for the functions in our classes. 2000 Mathematical Subject Classification: 30C45, 30C50, 31A05.

We consider encoding of a source with a pre-speciied second order statistics, but otherwise arbitrary, by Entropy Coded Dithered (lattice) Quantization (ECDQ) incorporating linear pre-and post-lters. In the design and analysis of this scheme we utilize the equivalent additive noise channel model of the ECDQ. For Gaussian sources and square error distortion measure, the coding performance of the...